Proceedings of the International Congress of Mathematicians, 2 Teile: August 3-11, 1994 Zürich, Swit

Invited Forty-Five Minute Addresses at the Section Meetings.- Section 1. Logic.- New trends in partition calculus (Manuscript not submitted).- On the size of quotients by definable equivalence relations.- Model theory, differential algebra, and number theory.- Logic and complexity: Independence results and the complexity of propositional calculus.- Section 2. Algebra.- The path model for representations of symmetrizable Kac-Moody algebras.- Subgroup growth.- Constructions polynomiales et théorie de Galois.- Study of quadratic forms - Some connections with geometry.- Invariant differential operators.- Algebraic K-theory and motivic cohomology.- Modules of covariants.- Section 3. Number theory.- Linearized algebra (Manuscript not submitted).- Bounds for L-functions.- Polylogarithms in arithmetic and geometry.- Unexpected irregularities in the distribution of prime numbers.- Fonctions L p-adiques.- The role of smooth numbers in number theoretic algorithms.- Non-archimedean period domains.- Representations of Galois groups associated to modular forms.- Section 4. Geometry.- Einstein metrics and metrics with bounds on Ricci curvature.- Minimal foliations and laminations.- Harmonic maps, rigidity and Hodge theory.- Homological geometry and mirror symmetry.- Constant mean curvature surfaces in Euclidean spaces.- Intersection pairings on quotients and moduli spaces, and Witten's nonabelian localisation.- Anti-self-dual metrics and Kähler geometry.- The geometry of moduli spaces of vector bundles over algebraic surfaces.- Embedded surfaces and the structure of Donaldson's polynomial invariants (Manuscript not submitted).- Spaces with curvature bounded below.- Lagrangian intersections, 3-manifolds with boundary, and the Atiyah-Floer conjecture.- Generating functions, symplectic geometry and applications.- Section 5. Topology.- Smooth 4-manifolds and symplectic topology.- Topological modular forms, the Witten genus, and the theorem of the cube.- Applications dont la source est un classifiant.- Spaces of algebraic cycles: Levels of holomorphic approximation.- Dehn surgery on knots in the 3-sphere.- Cyclic splittings of finitely presented groups and the canonical JSJ-decomposition.- An algorithm to recognize the 3-sphere.- Characteristic classes, lattice points, and Euler-MacLaurin formulae.- Positive scalar curvature metrics - Existence and classification questions.- Nonlocally linear manifolds and orbifolds.- Section 6. Algebraic geometry.- Mumford-Stabilität in der algebraischen Geometrie.- Fundamental groups of curves in characteristic p.- Mixed motives, motivic cohomology, and Ext-groups.- Rational curves on algebraic varieties.- Some Eisenstein cohomology classes for the integral unimodular group.- Rigid and exceptional vector bundles and sheaves on a Fano variety.- Variations of Hodge structure and algebraic cycles.- Section 7. Lie groups and representations.- Genuine representations of the metaplectic group and epsilon factors.- The irreducible characters for semi-simple algebraic groups and for quantum groups.- Automorphic forms on Os+2,2(?)+ and generalized Kac-Moody algebras.- Spherical varieties.- Rigidity properties of group actions on CAT(0)-spaces.- Smooth representations of p-adic groups: The role of compact open subgroups.- Flows on homogeneous spaces and diophantine approximation.- Singular automorphic forms.- Gradings on representation categories.- Comparaison d'integrales orbitales pour des groupes p-adiques.- Section 8. Real and complex analysis.- L2-methods and effective results in algebraic geometry.- Meromorphic functions: Progress and problems.- Teichmüller space, dynamics, probability.- Fibering compact Kähler manifolds over projective algebraic varieties of general type.- Regularity of Fourier integral operators.- Finding structure in sets with little smoothness.- Topological, geometric, and complex analytic properties of Julia sets.- Smoothing estimates for the wave equation and applications.- A survey of M